Chapter Ten. Orthogonal groups

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Chapter Ten. Orthogonal groups

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"Chapter Ten. Orthogonal groups". Group Theory: Birdtracks, Lie's, and Exceptional Groups, Princeton: Princeton University Press, 2008, pp. 118-131. https://doi.org/10.1515/9781400837670.118

(2008). Chapter Ten. Orthogonal groups. In Group Theory: Birdtracks, Lie's, and Exceptional Groups (pp. 118-131). Princeton: Princeton University Press. https://doi.org/10.1515/9781400837670.118

2008. Chapter Ten. Orthogonal groups. Group Theory: Birdtracks, Lie's, and Exceptional Groups. Princeton: Princeton University Press, pp. 118-131. https://doi.org/10.1515/9781400837670.118

"Chapter Ten. Orthogonal groups" In Group Theory: Birdtracks, Lie's, and Exceptional Groups, 118-131. Princeton: Princeton University Press, 2008. https://doi.org/10.1515/9781400837670.118

Chapter Ten. Orthogonal groups. In: Group Theory: Birdtracks, Lie's, and Exceptional Groups. Princeton: Princeton University Press; 2008. p.118-131. https://doi.org/10.1515/9781400837670.118

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Kapitel in diesem Buch

Frontmatter i
Contents vii
Acknowledgments xi
Chapter One. Introduction 1
Chapter Two. A preview 5
Chapter Three. Invariants and reducibility 14
Chapter Four. Diagrammatic notation 27
Chapter Five. Recouplings 42
Chapter Six. Permutations 49
Chapter Seven. Casimir operators 60
Chapter Eight. Group integrals 76
Chapter Nine. Unitary groups 82
Chapter Ten. Orthogonal groups 118
Chapter Eleven. Spinors 132
Chapter Twelve. Symplectic groups 148
Chapter Thirteen. Negative dimensions 151
Chapter Fourteen. Spinors’ symplectic sisters 155
Chapter Fifteen. SU(n) family of invariance groups 162
Chapter Sixteen. G2 family of invariance groups 170
Chapter Seventeen. E8 family of invariance groups 180
Chapter Eighteen. E6 family of invariance groups 190
Chapter Nineteen. F4 family of invariance groups 210
Chapter Twenty. E7 family and its negative-dimensional cousins 218
Chapter Twenty-One. Exceptional magic 229
Appendix A. Recursive decomposition 237
Appendix B. Properties of Young projections 239
Bibliography 243
Index 259

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https://doi.org/10.1515/9781400837670.118

Kapitel in diesem Buch

Frontmatter i
Contents vii
Acknowledgments xi
Chapter One. Introduction 1
Chapter Two. A preview 5
Chapter Three. Invariants and reducibility 14
Chapter Four. Diagrammatic notation 27
Chapter Five. Recouplings 42
Chapter Six. Permutations 49
Chapter Seven. Casimir operators 60
Chapter Eight. Group integrals 76
Chapter Nine. Unitary groups 82
Chapter Ten. Orthogonal groups 118
Chapter Eleven. Spinors 132
Chapter Twelve. Symplectic groups 148
Chapter Thirteen. Negative dimensions 151
Chapter Fourteen. Spinors’ symplectic sisters 155
Chapter Fifteen. SU(n) family of invariance groups 162
Chapter Sixteen. G2 family of invariance groups 170
Chapter Seventeen. E8 family of invariance groups 180
Chapter Eighteen. E6 family of invariance groups 190
Chapter Nineteen. F4 family of invariance groups 210
Chapter Twenty. E7 family and its negative-dimensional cousins 218
Chapter Twenty-One. Exceptional magic 229
Appendix A. Recursive decomposition 237
Appendix B. Properties of Young projections 239
Bibliography 243
Index 259

Chapter Ten. Orthogonal groups

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